P8131 Biostatistics Methods II Homework 10


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Problem 1
Suppose we have the following data:
Group 1: 4, 12+, 15, 21+, 23
Group 2: 2, 6+, 8+, 10, 19
Test H0 : h1(t) = h2(t) for all t, H1 : h1(t) 6= h2(t) for some t using the log-rank
(Optional, PhD required) Please also do the calculation by hand, and check
your result.

Problem 2
Consider the kidtran dataset in the KMsurv package where the death times of
kidney transplant patients are reported. The patients can be classied by race
(1=white and 2=black) and gender (1=male and 2=female) into one of four
groups. Compare the survival curves for dierent races in each sex group.

Problem 3
Consider the larynx data in the KMsurv package. Let
Z1 = 1 if the patient is in stage II, 0 otherwise
Z2 = 1 if the patient is in stage III, 0 otherwise
Z3 = 1 if the patient is in stage IV, 0 otherwise
Z4 = age of the patient (in years):

Fit a proportional hazards model using the covariates Z1, Z2, Z3, Z4 and the
interaction term Z1 * Z4. Explain your results.

What is the relative risk of
dying for a stage II patient of age 50 as compared to a stage I patient of the
same age?